An Algebraic Approach to the Input/Output Description of Nonlinear Discrete-Time Systems

Given a nonlinear discrete-time system described by analytic functions, a functional expansion of the output is proposed. In the general case a formula is derived in terms of tensor products of differential operators. When the controls act linearly or in case of systems given by polynomial difference equations, this development yields a discrete-time Volterra series. In that case, the Volterra kernels can be explicitly exhibited by means of straightforward algebraic computations.